What is the difference between face value and market value in stocks?

Face value (also called par value or nominal value) is the original printed value of a share, typically Rs 10 or Rs 100. Market value (or stock price) is the current price at which the share is traded in the market. A share is said to be at par when market value = face value, at premium when market > face value, and at discount when market < face value.

What is dividend in stocks?

Dividend is the annual income paid by a company to its shareholders. It is expressed as a percentage of the face value. If a Rs 100 share pays a 12% dividend, the annual income is Rs 12 per share — regardless of the share's market price.

What is brokerage in stock transactions?

Brokerage is the commission paid to a broker for buying or selling shares. When buying, brokerage is added to the market price (effective cost = market value + brokerage). When selling, brokerage is deducted from the selling price.

What does 'a 15% stock at 120' mean?

It means: Face value = Rs 100, Dividend rate = 15% (so annual income = Rs 15), Current market price = Rs 120. To earn Rs 15 income, you must invest Rs 120.

Stocks and Shares — Formulas, Shortcuts, and Worked Examples | TNPSC, SSC, Bank

Q: What is dividend in stocks?

Dividend is the annual income paid by a company to its shareholders. It is expressed as a percentage of the face value. If a Rs 100 share pays a 12% dividend, the annual income is Rs 12 per share — regardless of the share's market price.

Q: What is brokerage in stock transactions?

Brokerage is the commission paid to a broker for buying or selling shares. When buying, brokerage is added to the market price (effective cost = market value + brokerage). When selling, brokerage is deducted from the selling price.

Q: What does 'a 15% stock at 120' mean?

It means: Face value = Rs 100, Dividend rate = 15% (so annual income = Rs 15), Current market price = Rs 120. To earn Rs 15 income, you must invest Rs 120.

Quick Concept Summary

Stocks and Shares are financial instruments. In aptitude, these problems test your ability to calculate income, investment, and yield from stock market scenarios.

Key Terms:

Term	Meaning
Face Value (FV)	Printed/nominal value of a share (usually Rs 10 or Rs 100)
Market Value (MV)	Current trading price of the share
At Par	MV = FV
At Premium	MV > FV
At Discount	MV < FV
Dividend	Annual income paid as % of FV
Yield / Return	Actual % return on investment (based on MV)
Brokerage	Commission paid to broker (% of MV)

Reading a stock notation: "15% stock at 120"

Face value = Rs 100 (assumed when not stated)
Dividend rate = 15% → Annual income = Rs 15 per share
Market price = Rs 120 → You pay Rs 120 to earn Rs 15/year

Key Formulas

What to Calculate	Formula
Annual income per share	(Dividend% × FV) / 100
Number of shares bought	Investment / MV
Total annual income	Number of shares × (Dividend% × FV/100)
Yield % (return on investment)	(Annual Income / Investment) × 100
Investment for target income	(Target income / Dividend%) × MV
Effective MV with brokerage (buying)	MV + Brokerage
Effective MV with brokerage (selling)	MV − Brokerage

Worked Examples

Example 1: Annual Income from Stock

Problem:
Find the annual income from Rs 7,200 invested in 8% stock at Rs 90.

Given:
  Investment = Rs 7,200
  Dividend = 8%, Face value = Rs 100
  Market price = Rs 90

Step 1: Find number of shares
  Number of shares = Investment / Market Price
  = 7200 / 90 = 80 shares

Step 2: Find income per share
  Income per share = 8% of Rs 100 = Rs 8

Step 3: Total annual income
  Total = 80 × 8 = Rs 640

Answer: Annual income = Rs 640

Alternative shortcut:
  Income = (Investment / MV) × Dividend% × FV
  = (7200/90) × 8% × 100 = 80 × 8 = Rs 640

Example 2: Yield Percentage

Problem:
Find the yield on a 12% stock quoted at Rs 80.

Given:
  Dividend = 12%, Face value = Rs 100
  Market price = Rs 80

Step 1: Annual income per share = 12% of 100 = Rs 12

Step 2: Investment per share = Rs 80

Step 3: Yield = (Income / Investment) × 100
  Yield = (12 / 80) × 100 = 15%

Answer: Yield = 15%

Insight: Buying below par (Rs 80 < Rs 100) gives higher yield.
When MV < FV → Yield > Dividend%
When MV > FV → Yield < Dividend%
When MV = FV → Yield = Dividend%

Example 3: Investment Required for Target Income

Problem:
How much should be invested in 9% stock at Rs 120 to earn Rs 1,350 per year?

Given:
  Dividend = 9%, FV = Rs 100
  Market Price = Rs 120
  Target income = Rs 1,350

Step 1: Income per share = 9% × 100 = Rs 9

Step 2: Number of shares needed
  = Target income / Income per share
  = 1350 / 9 = 150 shares

Step 3: Investment required
  = 150 × MV = 150 × 120 = Rs 18,000

Answer: Investment needed = Rs 18,000

Shortcut: Investment = (Target Income / Dividend%) × MV
  = (1350 / 9) × 120 = Rs 18,000

Example 4: Brokerage Included

Problem:
A person buys Rs 10,000 worth of 10% stock at Rs 125 with 2% brokerage.
Find the annual income.

Given:
  Investment = Rs 10,000
  Dividend = 10%, FV = Rs 100
  Market Price = Rs 125
  Brokerage = 2%

Step 1: Effective buying price per share
  Brokerage amount = 2% of 125 = Rs 2.50
  Effective price = 125 + 2.50 = Rs 127.50

Step 2: Number of shares
  = 10000 / 127.50 ≈ 78.43 ≈ 78 shares (whole shares only)

Step 3: Annual income
  = 78 × (10% of 100)
  = 78 × 10 = Rs 780

Answer: Annual income ≈ Rs 780

Example 5: Comparing Two Stocks

Problem:
Which is a better investment: 6% stock at Rs 120 or 4% stock at Rs 60?

Stock A: 6% at 120
  Yield A = (6/120) × 100 = 5%

Stock B: 4% at 60
  Yield B = (4/60) × 100 = 6.67%

Answer: Stock B (4% at 60) gives better yield (6.67% > 5%).

Key insight: Lower price with reasonable dividend = higher yield.

Example 6: Selling and Reinvesting

Problem:
A person sells Rs 5,000 worth of 8% stock at Rs 125 and reinvests the proceeds
in 10% stock at Rs 150. Find the change in income.

Step 1: Proceeds from sale
  Shares sold = 5000 / 125 = 40 shares
  Value received = 40 × 125 = Rs 5,000

Step 2: Old income
  = 40 × (8% × 100) = 40 × 8 = Rs 320

Step 3: New investment = Rs 5,000 in 10% stock at Rs 150
  New shares = 5000 / 150 = 33.33 ≈ 33 shares

Step 4: New income
  = 33 × (10% × 100) = 33 × 10 = Rs 330

Change in income = 330 − 320 = Rs +10 increase

Answer: Income increases by Rs 10.

Shortcuts and Tricks

Trick 1: The Yield Formula

Yield% = (Dividend% × FV) / MV

This is the single most useful formula. If FV = 100: Yield% = Dividend% × 100 / MV = Dividend% / (MV/100)

Trick 2: At What Price Is Yield Same as Dividend?

When MV = FV (at par). A 10% stock at Rs 100 yields exactly 10%.

Trick 3: Compare Investments Using Yield

Always compare stocks by yield, not by dividend rate. Higher yield = better investment.

Trick 4: Income Ratio

If you invest equal amounts in two stocks: Income ratio = Yield A : Yield B = (D₁/MV₁) : (D₂/MV₂)

TNPSC / SSC Exam Pattern

Question Type	Frequency	Difficulty
Find income from investment	Common	Medium
Find yield percentage	Common	Medium
Investment for target income	Common	Medium
Compare two stocks	Occasional	Medium
Problems with brokerage	Occasional	Medium–Hard

Practice Questions

Q1. Find the income from Rs 4,500 invested in 6% stock at Rs 90. Answer: Shares = 4500/90 = 50. Income = 50 × 6 = Rs 300

Q2. Find the yield on a 10% stock at Rs 125. Answer: Yield = (10/125) × 100 = 8%

Q3. A 5% stock at Rs 80 gives the same yield as a 4% stock at what price? Answer: Yield of 5% at 80 = (5/80)×100 = 6.25%. For 4% stock: 6.25 = (4/x)×100 → x = 400/6.25 = Rs 64

Q4. How much 8% stock at Rs 96 can be bought for Rs 4,800? Answer: Shares = 4800/96 = 50 shares. Face value total = 50 × 100 = Rs 5,000

Q5. How much must be invested in 12% stock at Rs 80 to earn Rs 600 a year? Answer: Investment = (600/12) × 80 = 50 × 80 = Rs 4,000

Q6. Which gives more income: Rs 1,800 in 6% stock at Rs 120 or Rs 1,800 in 5% stock at Rs 90? Answer: Stock A: income = (1800/120)×6 = 15×6 = Rs 90. Stock B: (1800/90)×5 = 20×5 = Rs 100. Stock B is better.

Q7. Find the annual income from Rs 9,000 in 7.5% stock at Rs 90. Answer: Shares = 9000/90 = 100. Income = 100 × 7.5 = Rs 750

Q8. A 10% stock bought at Rs 110 gives a yield of how much percent? Answer: Yield = (10/110) × 100 = 9.09%

Q9. To get 10% return, at what price should a 6% stock be bought? Answer: 10 = (6/x)×100 → x = 600/10 = Rs 60

Q10. A man sells Rs 5,000 of 6% stock at 87 and buys 5% stock at 100. Find change in income. Answer: Old income = 50×6 = Rs 300. Sale proceeds = 50×87 = Rs 4,350. New shares = 4350/100 = 43.5 → 43 shares. New income = 43×5 = Rs 215. Change = 215−300 = −Rs 85 decrease.